Estimate Square Roots | Interactive Worksheet - Free Printable

To solve the problem of estimating square roots by finding the two whole numbers between which each square root falls, we need to identify the perfect squares closest to the given numbers and determine the range.

Step-by-Step Solution:

#### 1. $\sqrt{5}$
- The perfect squares closest to 5 are $4$ and $9$.
- $\sqrt{4} = 2$ and $\sqrt{9} = 3$.
- Therefore, $\sqrt{5}$ is between $2$ and $3$.

#### 2. $\sqrt{12}$
- The perfect squares closest to 12 are $9$ and $16$.
- $\sqrt{9} = 3$ and $\sqrt{16} = 4$.
- Therefore, $\sqrt{12}$ is between $3$ and $4$.

#### 3. $\sqrt{34}$
- The perfect squares closest to 34 are $25$ and $36$.
- $\sqrt{25} = 5$ and $\sqrt{36} = 6$.
- Therefore, $\sqrt{34}$ is between $5$ and $6$.

#### 4. $\sqrt{23}$
- The perfect squares closest to 23 are $16$ and $25$.
- $\sqrt{16} = 4$ and $\sqrt{25} = 5$.
- Therefore, $\sqrt{23}$ is between $4$ and $5$.

#### 5. $\sqrt{101}$
- The perfect squares closest to 101 are $100$ and $121$.
- $\sqrt{100} = 10$ and $\sqrt{121} = 11$.
- Therefore, $\sqrt{101}$ is between $10$ and $11$.

#### 6. $\sqrt{69}$
- The perfect squares closest to 69 are $64$ and $81$.
- $\sqrt{64} = 8$ and $\sqrt{81} = 9$.
- Therefore, $\sqrt{69}$ is between $8$ and $9$.

#### 7. $\sqrt{47}$
- The perfect squares closest to 47 are $36$ and $49$.
- $\sqrt{36} = 6$ and $\sqrt{49} = 7$.
- Therefore, $\sqrt{47}$ is between $6$ and $7$.

#### 8. $\sqrt{96}$
- The perfect squares closest to 96 are $81$ and $100$.
- $\sqrt{81} = 9$ and $\sqrt{100} = 10$.
- Therefore, $\sqrt{96}$ is between $9$ and $10$.

#### 9. $\sqrt{125}$
- The perfect squares closest to 125 are $121$ and $144$.
- $\sqrt{121} = 11$ and $\sqrt{144} = 12$.
- Therefore, $\sqrt{125}$ is between $11$ and $12$.

#### 10. $\sqrt{116}$
- The perfect squares closest to 116 are $100$ and $121$.
- $\sqrt{100} = 10$ and $\sqrt{121} = 11$.
- Therefore, $\sqrt{116}$ is between $10$ and $11$.

#### 11. $\sqrt{77}$
- The perfect squares closest to 77 are $64$ and $81$.
- $\sqrt{64} = 8$ and $\sqrt{81} = 9$.
- Therefore, $\sqrt{77}$ is between $8$ and $9$.

#### 12. $\sqrt{142}$
- The perfect squares closest to 142 are $121$ and $144$.
- $\sqrt{121} = 11$ and $\sqrt{144} = 12$.
- Therefore, $\sqrt{142}$ is between $11$ and $12$.

Final Answer:

\[
\boxed{
\begin{array}{ll}
1. \sqrt{5} \text{ is between } 2 \text{ and } 3. & 2. \sqrt{12} \text{ is between } 3 \text{ and } 4. \\
3. \sqrt{34} \text{ is between } 5 \text{ and } 6. & 4. \sqrt{23} \text{ is between } 4 \text{ and } 5. \\
5. \sqrt{101} \text{ is between } 10 \text{ and } 11. & 6. \sqrt{69} \text{ is between } 8 \text{ and } 9. \\
7. \sqrt{47} \text{ is between } 6 \text{ and } 7. & 8. \sqrt{96} \text{ is between } 9 \text{ and } 10. \\
9. \sqrt{125} \text{ is between } 11 \text{ and } 12. & 10. \sqrt{116} \text{ is between } 10 \text{ and } 11. \\
11. \sqrt{77} \text{ is between } 8 \text{ and } 9. & 12. \sqrt{142} \text{ is between } 11 \text{ and } 12. \\
\end{array}
}
\]